t^3+3t^2+8t=0

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Solution for t^3+3t^2+8t=0 equation: 


Simplifying
t3 + 3t2 + 8t = 0

Reorder the terms:
8t + 3t2 + t3 = 0

Solving
8t + 3t2 + t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(8 + 3t + t2) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

Move all terms containing t to the left, all other terms to the right.

Simplifying
t = 0

Subproblem 2
Set the factor '(8 + 3t + t2)' equal to zero and attempt to solve:

Simplifying
8 + 3t + t2 = 0

Solving
8 + 3t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 3t + -8 + t2 = 0 + -8

Reorder the terms:
8 + -8 + 3t + t2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3t + t2 = 0 + -8
3t + t2 = 0 + -8

Combine like terms: 0 + -8 = -8
3t + t2 = -8

The t term is 3t.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3t + 2.25 + t2 = -8 + 2.25

Reorder the terms:
2.25 + 3t + t2 = -8 + 2.25

Combine like terms: -8 + 2.25 = -5.75
2.25 + 3t + t2 = -5.75

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {0}

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